EngineeringFormulaEngineering Mechanics
Free Fall Calculator
Calculate drop distance, fall time, impact speed from time or height, or vertical-motion values for ideal free fall with negligible air resistance.
Free fall describes one-dimensional vertical motion under gravity alone, with air resistance neglected. This calculator covers two common cases: an object dropped from rest, and an object released with an initial vertical velocity. Choose the mode that matches your problem, then solve for the missing time, distance, speed, or velocity term using standard free-fall equations.
g · Positive magnitude of the local gravitational acceleration.
t · Elapsed time during the free-fall interval.
Dropped-from-rest mode treats distance and speed as positive magnitudes. Use it for classic release-and-fall problems with zero initial velocity.
Solution
Enter the required values to calculate drop distance.
Formula Sheet
- gGravity
- tTime Interval
- hDrop Distance
- yVertical Displacement
- vVelocity
- uInitial Velocity
Variables & Units
| Symbol | Variable | Description | Common Units |
|---|---|---|---|
| g | Gravity | Positive magnitude of the local gravitational acceleration. | m/s², ft/s², g |
| t | Time Interval | Elapsed time during the free-fall portion of the motion. | ms, s, min |
| h | Drop Distance | Vertical distance fallen in dropped-from-rest mode. | cm, m, ft |
| y | Vertical Displacement | Signed vertical displacement in the upward-positive sign convention. | cm, m, ft |
| v | Velocity | Impact speed magnitude in dropped mode, or signed final velocity in initial-velocity mode. | m/s, km/h, mph, ft/s |
| u | Initial Velocity | Velocity at the instant the free-fall interval begins. | m/s, km/h, mph, ft/s |
How to Use This Calculator
- 01Choose the motion type first. Use Dropped from Rest when the object is simply released. Use Initial Vertical Velocity when the object is thrown upward or downward before free fall begins.
- 02Select which variable to solve for. The calculator will show only the inputs required for that equation. In dropped-from-rest mode, impact speed can be solved from either fall time or drop distance.
- 03Enter the known values with their units, then select Calculate to see the answer in base SI units, the active formula, and the substitution.
- 04Dropped-from-rest mode uses magnitudes only. Initial-velocity mode uses the upward-positive sign convention: upward velocity is positive, downward velocity is negative, and gravity is entered as a positive magnitude acting downward. Use the result as ideal motion only; real impact force depends on stopping distance or stopping time.
How the Formula Works
For an object dropped from rest, the initial velocity is zero and the only acceleration is gravity. Under those assumptions, the drop distance after time t is h = 1/2 g t² and the speed magnitude can be found from either v = g t or v = √(2 g h). Because gravity is constant near Earth's surface, the distance grows with the square of time while speed grows linearly with time.
For vertical free fall with an initial velocity, the same constant-gravity model applies but the object may begin moving upward or downward. Using upward as the positive direction gives v = u - g t and y = u t - 1/2 g t². This lets the calculator handle throws upward, throws downward, and releases from height, as long as air resistance remains negligible.
Worked Example 01
Drop distance after 3 seconds
Known
- Gravity (g): 9.81 m/s²
- Time (t): 3 s
Formula
h = 1/2 g t²
Substitution
h = 1/2 × 9.81 × 3²
Result
h = 44.145 m
An object dropped from rest falls 44.145 m in 3 s when gravity is 9.81 m/s² and air resistance is neglected.
Worked Example 02
Fall time from a 45 m drop
Known
- Drop Distance (h): 45 m
- Gravity (g): 9.81 m/s²
Formula
t = √(2 h / g)
Substitution
t = √((2 × 45) / 9.81)
Result
t ≈ 3.03 s
A 45 m free fall from rest takes a little over 3 seconds under standard near-Earth gravity.
Worked Example 03
Impact speed from a known drop height
Known
- Drop Distance (h): 45 m
- Gravity (g): 9.81 m/s²
Formula
v = √(2 g h)
Substitution
v = √(2 × 9.81 × 45)
Result
v ≈ 29.71 m/s
A dropped object falling 45 m reaches an impact speed of about 29.71 m/s when air resistance is neglected.
Worked Example 04
Final velocity of an object thrown upward
Known
- Initial Velocity (u): 20 m/s
- Gravity (g): 9.81 m/s²
- Time (t): 3 s
Formula
v = u - g t
Substitution
v = 20 - (9.81 × 3)
Result
v = -9.43 m/s
The negative sign means the object is moving downward after 3 s if upward is taken as positive.
Worked Example 05
Vertical displacement during upward throw
Known
- Initial Velocity (u): 20 m/s
- Gravity (g): 9.81 m/s²
- Time (t): 3 s
Formula
y = u t - 1/2 g t²
Substitution
y = (20 × 3) - (1/2 × 9.81 × 3²)
Result
y = 15.855 m
After 3 s the object is still 15.855 m above its release point, even though it is already moving downward.
Applications
- 01Estimating fall time, drop distance, or impact speed in introductory mechanics problems
- 02Checking vertical throw and release calculations under a constant-gravity assumption
- 03Comparing how different local gravity values affect otherwise similar free-fall motions
- 04Estimating ideal impact speed before passing the result to kinetic-energy or impact-force calculations
Assumptions
- 01Air resistance, drag, and buoyancy are neglected.
- 02Gravity is treated as constant over the motion interval.
- 03The motion is one-dimensional and vertical.
Where This Model Stops
- 01Not suitable for long falls where air resistance becomes important; a terminal-velocity or drag model is needed there.
- 02Does not model bounces, impacts, changing gravitational fields, or two-dimensional projectile motion.
- 03Does not turn impact speed into injury, damage, or force estimates; use impact-energy/impact-force methods with stopping distance for that.
References
- [1]3.5 Free Fall
OpenStax University Physics Volume 1
Presents the standard one-dimensional free-fall equations and sign-convention guidance.
- [2]NIST Guide to the SI, Appendix B.9
NIST
Lists the standard acceleration of free fall g_n = 9.80665 m/s² used in engineering and unit conversion work.
Frequently Asked Questions
Does free fall always mean an object is moving downward?
No. In mechanics, free fall means gravity is the only significant force. An object thrown upward is still in free fall after release because gravity alone determines its motion.
Why does this calculator ignore air resistance?
Because the textbook free-fall equations assume constant gravity and negligible drag. Once air resistance matters, acceleration is no longer constant and a drag-based model is needed.
How is this different from the Velocity or Acceleration Calculator?
This page specializes those general kinematics relationships to gravity-driven vertical motion. It adds free-fall framing, drop-specific formulas, and sign-convention guidance that generic velocity or acceleration tools do not provide.
Can I use impact speed as impact force?
No. Impact speed tells you how fast the object is moving just before contact. Impact force depends on how quickly or over what distance the object stops, so two objects with the same impact speed can produce very different forces.